Jeff Skinner's 29th goal of the season gave the Canes a 1-0 lead late in the second period, but a Skinner turnover soon set up a tying score for the Jackets.
Skinner scored with 3:31 left in the second. Riley Nash passed from the left wing to Skinner in the slot for a shot that was stopped. But Elias Lindholm got a piece of the puck in front of the crease and Skinner chipped it in over a fallen David Savard of Columbus.
But Skinner's turnover in the offensive zone allowed the Jackets to easily tie the score. Matt Calvert picked off Skinner's pass from the corner and quickly whipped a wrister past goalie Anton Khudobin with 1:14 remaining in the period.
The Canes and Blue Jackets were scoreless after a tight-checking, evenly-played and well-played first period.
The Jackets outshot the Canes 11-7 in the first and Khudobin had the most sparkling save of the period, denying Blake Comeau on a two-on-one rush with 6:30 left.
Curtis McElhinney made his third straight start for the Jackets as Sergei Bobrovsky recovers from the flu. Bobrovsky took shots at the morning skate Saturday but is serving as the backup.
McElhinney made sharp stops against Jordan Staal and then Eric Staal in the first three minutes of the game.
The Jackets, clinging to a wild-card playoff spot, played Friday night in Pittsburgh, losing 2-1.
Khudobin was coming off a 3-0 shutout of the Florida Panthers on Thursday, and had a career-high 46 saves against Columbus on March 18 as the Canes took a 3-1 road win.